Schema Analysis of the Traveling Salesman Problem Using Genetic Algorithms

This paper provides a substantial proof th at genet ic algorithms (GAs) work for t he traveling salesman problem (TSP) . The method introduced is based on an adjacency matrix representation of the TSP t hat allows t he GA to manipulate edges while using conventional crossover. This combination, interleaved with invers ion (2-opt), allows th e GA to rapidly discover the best known solutions t o seven of the eight TS P test problems frequentl y st udied in t he lit erature. (The GA solut ion is within 2% of t he best known solution for t he eighth problem.) T hese results st and in contrast to earli er t ent ative conclusions that GAs are ill-suited to solving TSP problems, and suggest that the performance of probabilisti c search algorithms (such as GAs) is highly dependent on representation and t he choice of neighborhood operators.